(4x-7)(6x-9)=118

Solution for (4x-7)(6x-9)=118 equation:

(4x-7)(6x-9)=118

We move all terms to the left:

(4x-7)(6x-9)-(118)=0

We multiply parentheses ..

(+24x^2-36x-42x+63)-118=0

We get rid of parentheses

24x^2-36x-42x+63-118=0

We add all the numbers together, and all the variables

24x^2-78x-55=0

a = 24; b = -78; c = -55;
Δ = b2-4ac
Δ = -782-4·24·(-55)
Δ = 11364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{11364}=\sqrt{4*2841}=\sqrt{4}*\sqrt{2841}=2\sqrt{2841}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{2841}}{2*24}=\frac{78-2\sqrt{2841}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{2841}}{2*24}=\frac{78+2\sqrt{2841}}{48}
$